Correlation filters have been traditionally used for a variety of pattern matching problems including the recognition of mobile objects for automatic target recognition. The matched filter is perhaps the earliest and simplest of all correlation filters. A variety of design techniques have been proposed in the literature to extend this fundamental concept. B. V. K. Vijaya Kumar, "Tutorial survey of composite filter designs for optical correlators", Applied Optics, Vol. 31, pp. 4773-4801, (1992). A popular approach is to treat the filter as a composite of several samples of the pattern to be recognized (known as training images) . Unconstrained Correlation Filters (UCFs), (see, A. Mahalanobis, B. V. K. Vijaya Kumar, and D. Casasent, "Minimum average correlation energy filters", Applied Optics, Vol. 26, pp. 3633-3640 (1987)), are the most recent development in composite filter design. These filters are derived to analytically optimize a suitable performance criterion. As the name indicates, a key difference between UCFs and their predecessors (known as synthetic discriminant filters or SDFS) is that no hard constraints are placed on the training data.
The early SDFs were designed to control only one point in the correlation plane. Unfortunately, this strategy seems inadequate because either large sidelobes make this controlled point difficult to find, or its value is significantly different from the desired value specified in the training process. It has been suggested that perhaps performance can be improved if all points in the correlation plane are somehow taken into account. Indeed, the minimum average correlation energy (MACE) filter (A. Mahalanobis, B. V. K. Vijaya Kumar, and D. Casasent, "Minimum average correlation energy filters", Applied Optics, Vol. 26, pp. 3633-3640 (1987)) affects the entire correlation plane by suppressing sidelobes everywhere. However, a more systematic development is needed to translate correlation plane control into improved discrimination and distortion tolerance.
The primary purpose of correlation filters is distortion-invariant recognition of objects in clutter. Traditionally, SDF filters have been designed by imposing linear constraints on the training images to yield a known value at a specific location in the correlation plane. However, such conditions do not explicitly control the filters' ability to generalize over the entire domain of the training images. Various filters exhibit different levels of distortion tolerance even with the same training set and constraints. Another reason to question the method of using hard constraints on the training images is that these conditions do not hold for the test images, and the outputs obtained from the filter in practice are almost certain to differ from the values specified during training. Based on these observations, the UCFs were designed in a major departure from conventional SDF filter design philosophy of which the MACE filter is a special case.